Once more nice equations for nice groups

Authors:
Shreeram S. Abhyankar and Paul A. Loomis

Journal:
Proc. Amer. Math. Soc. **126** (1998), 1885-1896

MSC (1991):
Primary 12F10, 14H30, 20D06, 20E22

DOI:
https://doi.org/10.1090/S0002-9939-98-04421-9

MathSciNet review:
1459101

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Abstract | References | Similar Articles | Additional Information

Abstract: In a previous paper, nice quintinomial equations were given for unramified coverings of the affine line in nonzero characteristic $p$ with the projective symplectic isometry group PSp$(2m,q)$ and the (vectorial) symplectic isometry group Sp$(2m,q)$ as Galois groups where $m>2$ is any integer and $q>1$ is any power of $p$. Here we deform these equations to get nice quintinomial equations for unramified coverings of the once punctured affine line in characteristic $p$ with the projective symplectic similitude group PGSp$(2m,q)$ and the (vectorial) symplectic similitude group GSp$(2m,q)$ as Galois groups.

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Additional Information

**Shreeram S. Abhyankar**

Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47907

Email:
ram@cs.purdue.edu

**Paul A. Loomis**

Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47907

Email:
loomisp@math.purdue.edu

Received by editor(s):
December 1, 1996

Additional Notes:
The first author’s work was partly supported by NSA grant MDA 904-97-1-0010, and the second author’s work was partly supported by a PRF grant at Purdue University.

Communicated by:
Ronald M. Solomon

Article copyright:
© Copyright 1998
American Mathematical Society